Sounds like you may have a problem with badly packaged video that's throwing wrenches in PrPro's system... Try using a program like FFMPEG to repackage the video files and give it new headers... that may help. Or before you go that route, right click on the footage in your bin and choose "interpret" and manually set the frame rate for your footage so that it's forced to be a consistent rate... that may help as well, or it may totally break it. Worth a shot, though...
Welcome to the forum.
I agree with you and David, that the variable Frame Rate is the issue. That might be fine for playback, in a player, that can handle the variable Frame Rate, but not for editing, where you have a fixed Frame Rate.
I would try David's suggestion, and hope that the conversion will maintain sync, while giving you a constant Frame Rate.